Position change of body in non-isolated system

In summary, a body of mass 5 kg is initially at rest and a constantly increasing force is applied to it for 7.5 seconds according to F(t)=at, where a is a constant of 0.866 N/s. The distance x the body travels during the application of the force can be determined by finding the velocity and displacement using Newton's Laws and integration. The acceleration is given by force/mass and the velocity and displacement can be found by integrating the acceleration and velocity equations, respectively.
  • #1
meathead
1
0

Homework Statement



A body of mass 5 kg is initially at rest. At time t=0, a constantly increasing force is applied to the body for 7.5 seconds according to:F(t)=at; where a is a constant 0.866 N/s. Determine the distance x the body travels during the application of the force.

Homework Equations


delta E of system = sigma T
sum of forces in y direction =0
normal force - mass*gravitational acceleration=0
work=force*change in position
1/2mass*final velocity^2 = 1/2mass*initial velocity^2 + work

The Attempt at a Solution



At kind of a loss for where to start this problem because the force is not constant.
Can I some how find a value for Work and use that to solve for final velocity and use that to find change in position? Please Help!
 
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  • #2
You can not use the work-energy theorem in this problem.
Use Newton's Law: the acceleration is force/mass. Now the acceleration depends on time. Acceleration is the time derivative of velocity; you get velocity by integrating acceleration:

[tex] v(t) = \int{a(t)dt}[/tex]

the integration constant is detemined from the condition v(0)=0.
Velocity is the time derivative of displacement: you get the displacement by integrating velocity: v(t)

[tex] x(t=7.5) -x(0) = \int_0^{t=7.5}{v(t)dt}[/tex]



ehild
 
  • #3


I would approach this problem by first analyzing the given information and identifying the relevant equations and principles to use. In this case, we are dealing with a non-isolated system (since an external force is being applied) and we are interested in determining the position change of the body.

To start, we can use the equation for work, W = F*d, where F is the force and d is the distance traveled. Since we know the force, F(t) = at, we can integrate this equation to find the work done over the given time period of 7.5 seconds:

W = ∫ F(t) dt = ∫ at dt = (1/2)at^2

Plugging in the given values, we get W = (1/2)(0.866 N/s)(7.5 s)^2 = 24.56 J

Next, we can use the equation for kinetic energy, KE = (1/2)mv^2, to find the final velocity of the body. Since the body is initially at rest, we can set the initial kinetic energy to zero and solve for the final velocity:

KE = (1/2)mv^2 = W
v = √(2W/m) = √(2*24.56 J/5 kg) = 2.48 m/s

Finally, we can use the equation for position change, Δx = v*t, to find the distance traveled by the body:

Δx = v*t = (2.48 m/s)(7.5 s) = 18.6 m

Therefore, the body travels a distance of 18.6 meters during the application of the force.

In summary, as a scientist, I would approach this problem by identifying the relevant equations and principles to use and then applying them step by step to find the solution. By using the equations for work, kinetic energy, and position change, we were able to determine the distance traveled by the body in this non-isolated system.
 

FAQ: Position change of body in non-isolated system

1. What is the definition of "position change of body in non-isolated system"?

The position change of body in non-isolated system refers to the movement or displacement of an object within a system that is affected by external forces or influences.

2. How is the position change of body in non-isolated system different from isolated system?

In an isolated system, the object's movement or displacement is not affected by any external forces, while in a non-isolated system, the object's movement is influenced by external factors.

3. What are some examples of non-isolated systems in which position change of body can occur?

Some examples of non-isolated systems include a car driving on a road, a ball being thrown in the air, and a pendulum swinging back and forth.

4. How can the position change of body in non-isolated system be calculated?

The position change of body in non-isolated system can be calculated using principles of physics, such as Newton's laws of motion, and by considering the external forces and influences acting on the object.

5. Why is it important to consider the position change of body in non-isolated system in scientific studies?

Understanding the position change of body in non-isolated systems is crucial in many scientific studies, as it allows for the prediction and analysis of movement and behavior of objects in real-world scenarios.

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